Circle formulas
| To find | From radius r | From diameter d |
|---|
| Circumference | 2πr | πd |
| Area | πr² | πd² ÷ 4 |
| Radius from circumference | C ÷ 2π |
| Radius from area | √(A ÷ π) |
Everyday uses
- Bike wheels: a 26-inch wheel travels about 81.7 inches (6.8 feet) per turn.
- Trees: foresters measure trunk circumference with a tape, then divide by π to get diameter.
- Crafts and sewing: how much trim goes around a round tablecloth or lampshade.
- Garden beds: edging needed for a circular flower bed.
Why π?
For every circle, the circumference divided by the diameter is the same number: π, about 3.14159. It never ends or repeats, which is why calculators use a long approximation. For school work, 3.14 or 22/7 is usually close enough.
Working out other shapes? Try the area calculator or the volume calculator for cylinders and spheres.
Last reviewed October 2026.
Frequently asked questions
What is the formula for circumference?
Circumference = 2 × π × radius, or π × diameter. With a radius of 5 inches, the circumference is 2 × 3.14159 × 5 ≈ 31.42 inches.
How do I find the diameter from the circumference?
Divide the circumference by π. A tree trunk with a circumference of 94 inches has a diameter of about 94 ÷ 3.14159 ≈ 29.9 inches. Choose "Circumference" as the known value and the calculator does this for you.
What is the difference between radius and diameter?
The radius is the distance from the center to the edge. The diameter goes all the way across through the center, so it is twice the radius.
What value of π does this use?
It uses JavaScript's built-in value of π, accurate to about 15 decimal places (3.141592653589793). Using 3.14 by hand will give slightly different answers.
How is circumference different from area?
Circumference is the distance around the circle, measured in units like inches or meters. Area is the space inside, measured in square units. Area = π × radius².